State-space recursive least-squares (SSRLS) is a new addition to the family of RLS adaptive filters. Beginning with a review of SSRLS, we show that this time-varying filter converges to an LTI (linear time invariant) filter. With observation noise as the input, BIBO (bounded input, bounded output) stability of the estimator is discussed next. We carry out the convergence analysis of SSRLS and its steady-state counterpart. Our discussion includes convergence in mean, mean-square error, mean-square deviation and learning curves. This development is imperative for a complete understanding of SSRLS to aid a designer to make the best use of the filter in advanced applications and analysis.